Question: Simplify the following expression: $ q = \dfrac{-2}{z + 1} + \dfrac{7}{4} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-2}{z + 1} \times \dfrac{4}{4} = \dfrac{-8}{4z + 4} $ Multiply the second expression by $\dfrac{z + 1}{z + 1}$ $ \dfrac{7}{4} \times \dfrac{z + 1}{z + 1} = \dfrac{7z + 7}{4z + 4} $ Therefore $ q = \dfrac{-8}{4z + 4} + \dfrac{7z + 7}{4z + 4} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-8 + 7z + 7}{4z + 4} $ $q = \dfrac{7z - 1}{4z + 4}$